I think I have located which application is causing the problem. I reinstalled Arch on the same system but a different HDD, and got openbox working together with lxdm display manager. I installed tint2 and Conky, and had them load at startup using ~/.config/openbox/autostart.sh. I logged out, but Conky appeared at the lxdm login screen, and lxdm failed to log in next time I tried.
I have been trying to fix this using the single.user mode for a while now. X starts when I run startx and get into the default twm environment. If I use startx to start openbox, it does not load my config files properly, and therefore starts with standard menu and theme. If I start openbox or openbox-session from terminal, I get the following error:
Openbox-Message: Kunde inte öppna en display från miljövariabeln DISPLAY.
Openbox-Message: Could not open display from DISPLAY environment variable.
I have been googling for a couple of hours, but without finding anything useful. I have read some suggestions that I should write a custom xorg.conf, but I have absolutely no idea what to put in it to get openbox running.